In signalling networks, the presence of multi-part activations/inhibitions and multimolecular reactions results in a highly branched structure. We give a theoretical framework, an algorithm and its implementation - SigNetRouter - for untangling such networks and detecting routes starting with a given initial factor or ending with a desired target. The effects and reactions are here considered as irreversible. If all effects involved in the route are known qualitatively (activation versus inhibition) and both effects and reactions are monomolecular, we can deduce the total effect. The factors acting together and the targets affected on the same route are detected. The cycles and possibly missing reactions are determined. The minimal amounts of each metabolite (in numbers of molecules) required to "move" the signal through each route and the remaining number of molecules are reported. Some theoretical and biological examples, such as the B cell antigen receptor signalling network illustrate the concepts. (c) 2004 Elsevier Ltd. All rights reserved.